What is the difference between logarithmic decay vs exponential decay?I am a little unclear on whether they are distinctly different or whether this is a 'square is a rectangle, but rectangle is not necessarily a square' type of relationship.

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What is the difference between logarithmic decay vs exponential decay?I am a little unclear on whether they are distinctly different or whether this is a &#039;square is a rectangle, but rectangle is not necessarily a square&#039; type of relationship.

toriannucz · Accepted Answer

The &quot;Square is a rectangle&quot; relationship is an example where the square is a special case of a rectangle.&quot;Exponential decay&quot; gets its name because the functions used to model it are of the form   f  (  x  )  =  A      e          k      x        +  C where   A  &amp;gt;  0 and   k  &amp;lt;  0. (Other k&#039;s above 0 yield an increasing function, not a decaying one.)Similarly for &quot;logarithmic decay,&quot; it gets its name since its modeled with functions of the form   g  (  x  )  =  A  ln  ⁡  (  x  )  +  C where   A  &amp;lt;  0These two families of functions do not overlap, so neither is a special case of the other. The giveaway is that the functions with   ln  ⁡  (  x  )  aren&#039;t even defined on half the real line, whereas the exponential ones are defined everywhere.

letumsnemesislh · Accepted Answer

The natural logarithm and exponential are inverses of one another, so the associated slopes will also be inverses. If you put exponentially decaying data on a log plot, i.e. log of the exponential decaying data with the same input, you get a linear plot. If you put the logarithmic decaying plot on an exponential plot (exponential of the data), you get a linear plot, so the way they are decaying is exactly opposite.

What is the difference between logarithmic decay vs exponential decay? I

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